MGF1131 QUIZ 1: MATHEMATICS IN
CONTEXT ADVANCED
COMPREHENSIVE ASSESSMENT
QUESTIONS AND ANSWERS
1. If Set A = {2, 4, 6, 8} and Set B = {x | x is a prime number less than 10}, what is the
cardinality of the intersection of A and B?
A. 1
B. 0
C. 2
D. 4
Answer: A
Conceptual Explanation: Set B contains {2, 3, 5, 7}. The only common element between A
and B is {2}. Thus, the cardinality is 1.
2. Which of the following is the correct negation of the statement: ‘All students in the class
passed the exam’?
A. No students in the class passed the exam.
,B. Some students in the class passed the exam.
C. All students in the class failed the exam.
D. At least one student in the class did not pass the exam.
Answer: D
Conceptual Explanation: The negation of a universal statement ‘All are’ is the existential
statement ‘Some are not’ or ‘At least one is not’.
3. Calculate the total interest earned on a $5,000 deposit at an annual interest rate of 4%
compounded quarterly for 3 years.
A. $600.00
B. $5,634.13
C. $634.13
D. $624.32
Answer: C
Conceptual Explanation: Using A = P(1 + r/n)^(nt): A = 5000(1 + 0.04/4)^(4*3) =
5000(1.01)^12 ≈ 5634.13. Interest = 5634.13 - 5000 = 634.13.
4. In symbolic logic, which of the following represents the contrapositive of the conditional
statement p → q?
A. q → p
B. ~q → ~p
, C. ~p → ~q
D. ~q ∨ p
Answer: B
Conceptual Explanation: The contrapositive is formed by switching the hypothesis and
conclusion and negating both.
5. A set contains 6 distinct elements. How many proper subsets does this set have?
A. 64
B. 63
C. 32
D. 31
Answer: B
Conceptual Explanation: A set with n elements has 2^n subsets. Proper subsets exclude
the set itself, so 2^6 - 1 = 64 - 1 = 63.
6. Which logical connective is true only when both component statements are true?
A. Disjunction (OR)
B. Conjunction (AND)
C. Biconditional (IF AND ONLY IF)
D. Conditional (IF-THEN)
CONTEXT ADVANCED
COMPREHENSIVE ASSESSMENT
QUESTIONS AND ANSWERS
1. If Set A = {2, 4, 6, 8} and Set B = {x | x is a prime number less than 10}, what is the
cardinality of the intersection of A and B?
A. 1
B. 0
C. 2
D. 4
Answer: A
Conceptual Explanation: Set B contains {2, 3, 5, 7}. The only common element between A
and B is {2}. Thus, the cardinality is 1.
2. Which of the following is the correct negation of the statement: ‘All students in the class
passed the exam’?
A. No students in the class passed the exam.
,B. Some students in the class passed the exam.
C. All students in the class failed the exam.
D. At least one student in the class did not pass the exam.
Answer: D
Conceptual Explanation: The negation of a universal statement ‘All are’ is the existential
statement ‘Some are not’ or ‘At least one is not’.
3. Calculate the total interest earned on a $5,000 deposit at an annual interest rate of 4%
compounded quarterly for 3 years.
A. $600.00
B. $5,634.13
C. $634.13
D. $624.32
Answer: C
Conceptual Explanation: Using A = P(1 + r/n)^(nt): A = 5000(1 + 0.04/4)^(4*3) =
5000(1.01)^12 ≈ 5634.13. Interest = 5634.13 - 5000 = 634.13.
4. In symbolic logic, which of the following represents the contrapositive of the conditional
statement p → q?
A. q → p
B. ~q → ~p
, C. ~p → ~q
D. ~q ∨ p
Answer: B
Conceptual Explanation: The contrapositive is formed by switching the hypothesis and
conclusion and negating both.
5. A set contains 6 distinct elements. How many proper subsets does this set have?
A. 64
B. 63
C. 32
D. 31
Answer: B
Conceptual Explanation: A set with n elements has 2^n subsets. Proper subsets exclude
the set itself, so 2^6 - 1 = 64 - 1 = 63.
6. Which logical connective is true only when both component statements are true?
A. Disjunction (OR)
B. Conjunction (AND)
C. Biconditional (IF AND ONLY IF)
D. Conditional (IF-THEN)
